"metatheorem" meaning in English

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  "etymology_text": "From meta- + theorem.",
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        {
          "ref": "2007, Nino B. Cocchiarella, Formal Ontology and Conceptual Realism, Springer Science & Business Media, →ISBN, page 224:",
          "text": "From these observations we conclude that we have the following metatheorem. Metatheorem 3: If φ is a theorem of second-order monadic predicate logic, then trs'(φ) is a theorem of our present conceptualist logic.",
          "type": "quote"
        },
        {
          "ref": "2008, Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas, Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems, Springer Science & Business Media, →ISBN, page 70:",
          "text": "The metatheorem of deduction will play an essential role ...",
          "type": "quote"
        },
        {
          "ref": "1977, Theory and decision:",
          "text": "This paper presents a metatheorem with the following property: Given a proven axiom-free lemma, which interrelates some of the elementary properties of a binary relation, the metatheorem mechanically transforms this lemma into its uniquely corresponding complementary lemma.",
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        "A statement about theorems proven in a metalanguage."
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        "(logic) A statement about theorems proven in a metalanguage."
      ],
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      ],
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        "metatheorem"
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  "word": "metatheorem"
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          "ref": "2007, Nino B. Cocchiarella, Formal Ontology and Conceptual Realism, Springer Science & Business Media, →ISBN, page 224:",
          "text": "From these observations we conclude that we have the following metatheorem. Metatheorem 3: If φ is a theorem of second-order monadic predicate logic, then trs'(φ) is a theorem of our present conceptualist logic.",
          "type": "quote"
        },
        {
          "ref": "2008, Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas, Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems, Springer Science & Business Media, →ISBN, page 70:",
          "text": "The metatheorem of deduction will play an essential role ...",
          "type": "quote"
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        {
          "ref": "1977, Theory and decision:",
          "text": "This paper presents a metatheorem with the following property: Given a proven axiom-free lemma, which interrelates some of the elementary properties of a binary relation, the metatheorem mechanically transforms this lemma into its uniquely corresponding complementary lemma.",
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      ],
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